Final answer:
A line is perpendicular to another line if and only if their slopes are negative reciprocals of each other. The given line equation is y = 2/3 x + 5. To find a line perpendicular to it, we need to find the negative reciprocal of the slope..
Step-by-step explanation:
The question asks for the equation of a line that is perpendicular to the line given by the equation y = 2/3x + 5. To find a perpendicular line, we need to determine the negative reciprocal of the slope of the given line. Since the slope of the given line is 2/3, the slope of a line perpendicular to it would be -3/2.
Using point-slope form, y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point the line goes through, and considering that our line can go through any point, we can select the origin for simplicity. Therefore, the equation can be written as y = -3/2x. Any line with this slope will be perpendicular to the given line regardless of its y-intercept.
A line is perpendicular to another line if and only if their slopes are negative reciprocals of each other. The given line equation is y = 2/3 x + 5. To find a line perpendicular to it, we need to find the negative reciprocal of the slope.
The slope of the given line is 2/3. The negative reciprocal of 2/3 is -3/2.
Therefore, an equation of a line perpendicular to y = 2/3 x + 5 would have a slope of -3/2. The y-intercept can be any value.